Date:         Thu, 14 Sep 2000 15:37:26 GMT
Reply-To:     z <gzuckier@MY-DEJA.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         z <gzuckier@MY-DEJA.COM>
Organization: Deja.com - Before you buy.
Subject:      Why offset in confidence interval for proportions?

Hi. This is more a stats question than a SAS one, but.... I'm trying to
wade through the JCAHO ORYX reporting requirements. Their formulae for
upper and lower limits for a 99% confidence interval for a proportion
are
U=((p+(Z^2)/(2n))+Z(root))/(1+(Z^2)/n)
L=((p+(Z^2)/(2n))-Z(root))/(1+(Z^2)/n)
where root=((z^2)/(4(n^2))+p(1-p)/n)^.5
Z=2.576
n=Number of patients
p=observed proportion

I can't exactly see where this comes from (I would have come up with
p(+or-)Z(p(1-p)/n)^.5 myself), and more to the point, this gives me a
confidence interval whose center is offset from p by the (Z^2)/2n term.
Waiting for the JCAHO to clarify is a slow process, in the meantime,
can anyone explain the theory behind this calculation? Thanks.


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